The sun radiates energy at the rate of 3.92x 10^26 W. (a) What is the change in the sun's mass in one second? (b)How much mass does the sun lose in the lifetime of your average earthling (say, 75 years)?
To answer both questions, we can use Einstein's famous equation: E = mc², where E represents energy, m represents mass, and c represents the speed of light.
(a) To find the change in the sun's mass in one second, we can use the equation E = mc² and rearrange it to solve for mass (m). The given energy radiated by the sun per second is 3.92x10^26 W.
Step 1: Convert the power from watts to joules using the relation 1 watt = 1 joule per second.
3.92x10^26 W = 3.92x10^26 J/s
Step 2: Since the energy (E) is given by the power (P) multiplied by time (t), we can rearrange the equation as E = Pt and solve for mass (m) using m = E/(c²).
(Energy) E = Pt
Mass (m) = E / (c²)
Plugging in the values:
Mass (m) = (3.92x10^26 J/s) / (speed of light)^2
The speed of light (c) is approximately equal to 3x10^8 m/s.
Mass (m) = (3.92x10^26 J/s) / (3x10^8 m/s)^2
Performing the calculation will give us the change in the sun's mass in one second.
(b) To calculate the mass the sun loses in the lifetime of an average earthling (75 years), we need to know the number of seconds in 75 years.
Step 1: Determine the number of seconds in one year.
There are 365.25 days in a year (accounting for leap years), and each day has 24 hours, each hour has 60 minutes, and each minute has 60 seconds.
Number of seconds in one year = 365.25 days × 24 hours × 60 minutes × 60 seconds
Step 2: Multiply the number of seconds in one year by 75 (representing the average earthling's lifetime) to find the total number of seconds in 75 years.
Total number of seconds in 75 years = Number of seconds in one year × 75
Finally, multiply the change in mass per second (from part a) by the total number of seconds to find the mass lost by the sun during an average earthling's lifetime.
Mass lost = Change in mass per second × Total number of seconds in 75 years
Performing the calculations will give us the mass the sun loses in an average earthling's lifetime.
Use the relationships
1 watt = 1 Joule / second
E = mc^2
E = energy, m = mass, c = speed of light (3*10^8 m/s)